Finance

AAL Move Probability $12.23 +0.12 (+0.9%)

Real historical back-data analysis: evaluates rolling trading-day windows to determine the probability of a stock touching or closing at your target move.

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Optional: Options Contract Breakeven & Edge Analysis — test a specific strike and premium
Touch Probability (First Passage)
23.3%
Stock touched +5.0% ($12.84) at least once during 2 trading days.
Median first touch: Day 2 of 2
Expiration Close Probability
11.3%
Stock closed at or beyond +5.0% at the end of the 2-day window.
The Touch Multiple
2.05x
You are 2.0x more likely to hit your target during the window than holding until expiration.
1σ Expected Move (68.3%)
±4.6%
$11.67 — $12.79

Historical 2-Day Return Distribution

Frequency of rolling 2-day percentage returns over 520 historical windows (2024-09-23 to 2026-10-21). The colored bar indicates the win zone for +5.0%.

-13.1% to -11.0%: 4 occurrences (0.8%) -12.1% -11.0% to -9.0%: 5 occurrences (1.0%) -9.0% to -6.9%: 14 occurrences (2.7%) -6.9% to -4.8%: 34 occurrences (6.5%) -5.8% -4.8% to -2.7%: 66 occurrences (12.7%) -2.7% to -0.6%: 101 occurrences (19.4%) -0.6% to +1.5%: 128 occurrences (24.6%) 0.5% +1.5% to +3.6%: 77 occurrences (14.8%) +3.6% to +5.7%: 46 occurrences (8.8%) +5.7% to +7.8%: 26 occurrences (5.0%) 6.7% +7.8% to +9.9%: 8 occurrences (1.5%) +9.9% to +11.9%: 5 occurrences (1.0%) +11.9% to +14.0%: 2 occurrences (0.4%) 13.0% +14.0% to +16.1%: 2 occurrences (0.4%) +16.1% to +18.2%: 1 occurrences (0.2%) +18.2% to +20.3%: 1 occurrences (0.2%) 19.3%
Historical returns Target move zone (+5.0%+) Target threshold bin

Probability Breakdown: Empirical vs. Theoretical Models

Comparing actual market back-data against Black-Scholes and Fat-Tail adjustments.

Model / Methodology Touch Probability Expiration Close Probability What It Tells You
Empirical Back-Data (Actual History) 23.3% 11.3% Model-free reality across 520 historical 2-day windows.
Fat-Tail Adjusted (Cornish-Fisher) — 7.2% Adjusts normal bell curve for real-world skewness (0.52) and kurtosis (5.13).
Standard Normal (Black-Scholes / GBM) 28.6% 14.3% Classic theoretical log-normal model with constant volatility (often underestimates tail risks).
Regime-Conditioned (Similar Volatility) 21.7% 10.9% Filters for historical windows that started with volatility similar to current 20-day HV (304 matching periods).

Underlying Volatility Profile

Volatility Metrics

  • 1-Year Annualized HV: 51.3%
  • Recent 20-Day HV: 38.4%
  • Parkinson Intraday Volatility: 39.5%
  • Vol Trend: Compressed (-25% vs baseline)

2-Day Return Quantiles

  • Median Return: -0.0%
  • Top 10% Move (90th percentile): +5.2%
  • Bottom 10% Move (10th percentile): -5.0%
  • Max Historical Gain (2d): +20.3%
  • Max Historical Loss (2d): -13.1%